Problem: What do the following two equations represent? $4x-2y = 5$ $-12x+6y = 1$
Putting the first equation in $y = mx + b$ form gives: $4x-2y = 5$ $-2y = -4x+5$ $y = 2x - \dfrac{5}{2}$ Putting the second equation in $y = mx + b$ form gives: $-12x+6y = 1$ $6y = 12x+1$ $y = 2x + \dfrac{1}{6}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.